I am trying to do a Quasi-Newton method with a basic cholesky adaptation, to guarantee B is positive definite. The code goes as follows:

```
function choleksyadaption!(A,β = 10e-3, max_iter = 1000)
@info "Adapting Cholesky Factorization to make Hessian positive definite."
if (isposdef(A))
return nothing
end
if any(diag(A) .<= 0)
τ = 0
else
τ = minimum(diag(A)) - β
end
for i in 1:max_iter
@info i τ, A
A = A + τ * I
if isposdef(A)
return nothing
else
τ = max(2 * τ, β)
end
end
return nothing
end
```

The problem is, in my eyes, that `isposidef`

, which calls `ishermitian`

requires the non diagonal elements to be exactly the same, which isn’t easy in numerics. For example

```
ishermitian([1 0.018511830506205723; 0.01851183050620573 1])
```

returns false, which makes sense, but I am unable to work with it. Is there a workarround, that I am missing?

Thanks!